Question

Find the number of faces, edges and vertices of the following polyhedrons and verify them by using Euler's formula.

(i) Tetrahedron

(ii) Octahedron

Answer 1

$\large \:(i){\underline{\boxed{\sf Tetrahedron}}}$

Number of Faces = 5

Number of Vertices = 6

Number of Edges = 9

Clearly, F + V = E + 2 i.e., 5 + 6 = 9 + 2

$\large \:(ii){\underline{\boxed{\sf Octahedron}}}$

Number of Faces = 8

Number of Vertices = 6

Number of Edges = 12

Clearly, F + V = E + 2 i.e., 8 + 6 = 12 + 2

Answer 2

Answer:

(i)

Tetrahedron

Number of Faces = 5

Number of Vertices = 6

Number of Edges = 9

Clearly, F + V = E + 2 i.e., 5 + 6 = 9 + 2

\large \:(ii){\underline{\boxed{\sf Octahedron}}}(ii)

Octahedron

Number of Faces = 8

Number of Vertices = 6

Number of Edges = 12

Clearly, F + V = E + 2 i.e., 8 + 6 = 12 + 2